Kevin is 30 years older than Umaima. For the last two years, Kevin and Umaima have been going to the same school. Twelve years ago, Kevin was 4 times older than Umaima. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and Umaima. Let Kevin's current age be $k$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $k = u + 30$ Twelve years ago, Kevin was $k - 12$ years old, and Umaima was $u - 12$ years old. The information in the second sentence can be expressed in the following equation: $k - 12 = 4(u - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = k - 30$ . Substituting this into our second equation, we get the equation: $k - 12 = 4($ $(k - 30)$ $ -$ $ 12)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 12 = 4k - 168$ Solving for $k$ , we get: $3 k = 156$ $k = 52$.